1. Field of the Disclosure
The present invention relates to a technique for interpolating high-frequency components of audio.
2. Description of the Related Art
There are known techniques for interpolating high-frequency components of audio, examples of which include techniques using fractal interpolation functions (FIFs) (for example, Japanese Unexamined Patent Application Publication Nos. 2005-084370, 2006-330144, and 2009-229492).
An FIF is used in a technique for, as illustrated in FIG. 6, interpolating a contraction mapping ωi(S) of a signal S for a time interval T of audio data, as a signal for an interpolation interval ti that is one of a plurality of time segments into which the time interval T is divided at a time position Xi for samples located at predetermined intervals as a division point, to upsample the audio data to interpolate high-frequency components of audio.
A known technique for upsampling audio data by using FIFs to interpolate high-frequency components of audio is a technique for, when the upper limit of the frequency range of audio indicated by input audio data is less than one half of the sampling rate of the audio data, downsampling the audio data to reduce the sampling rate of the audio data to one half, and then, upsampling the downsampled audio data using an FIF to interpolate high-frequency components of audio (Japanese Unexamined Patent Application Publication No. 2006-119524).
The upper limit of the frequency range of audio indicated by audio data having a sampling rate Fs is equal to Fs/2 according to Nyquist's theorem. For some audio data, such as audio data provided in compressed and encoded form, however, the upper limit of the frequency range of audio indicated by the audio data, which has a sampling rate Fs, is often less than Fs/2.
Even when the technique described above for downsampling input audio data to reduce the sampling rate of the input audio data to one half and then performing upsampling by using an FIF to interpolate high-frequency components of audio is applied, if an upper limit Fmax of the frequency range of audio indicated by the input audio data is less than one half of a sampling rate Fs of the downsampled audio data, the downsampled audio data does not include frequency components between the upper limit Fmax and the value Fs/2. Thus, a phenomenon occurs that, as illustrated in FIG. 7A, high-frequency components around the upper limit Fmax of the frequency range of the audio indicated by the audio data are lost without being interpolated.
FIG. 7A illustrates a case where audio data has a sampling rate of 96 kHz, the upper limit of the frequency range of audio indicated by the audio data is 20 kHz, downsampled audio data has a sampling rate of 48 kHz, and audio data upsampled by using an FIF has a sampling rate of 96 kHz. In FIG. 7A, SI represents a frequency characteristic of audio data and SO represents a frequency characteristic of audio data whose high-frequency components have been interpolated by using an FIF.